The circles `x^(2)+y^(2)-4x-6y-12=0` and `x^(2)+y^(2)+4x+6y+4=0`

Find the equation of the circle through the points of interrection of the circles x^(2)+y^(2)-4x-6y-12=0 and x^(2)+y^(2)+6x+4y-12=0 and cutting the circle x^(2)+y^(2)-2x-4=0 orthogonally.

The number of common tangents to the circles x^(2)+y^(2)-4x-6y-12=0 and x^(2)+y^(2)+6x+18y+26=0 , is

The number of common tangents to the circles x^(2)+y^(2)-4x-6y-12=0 and x^(2)+y^(2)+6x+18y+26=0 , is -

The number of common tangents to the circles x^(2)+y^(2)-4x-6y-12=0 and x^(2)+y^(2)+6x+18y+26=0 , is

The number of common tangents to the circles x^(2)+y^(2)-4x-6y-12=0 and x^(2)+y^(2)+6x+18y+26=0 , is

The number of common tangents to the circles x^(2)+y^(2)-4x-6y-12=0 and x^(2)+y^(2)+6x+18y+26=0 , is

Find the locus of the centres of the circle which cut the circles x^(2)+y^(2)+4x-6y+9=0 and x^(2)+y^(2)+4x+6y+4=0 orthogonally